Extended Nielsen transformations and triviality of a group
It was conjectured by \textit{J. J. Andrews} and \textit{M. L. Curtis} [Proc. Am. Math. Soc. 16, 192-195 (1965; Zbl 0131.38301) and Am. Math. Mon. 73, 21-28 (1966; Zbl 0135.044)] that if the trivial group has a finite balanced presentation \(<x_ 1,...,x_ n|\) \(r_ 1,...,r_ n>\) then \(\{r_ 1,...,r_ n\}\) can be transformed into \(\{x_ 1,...,x_ n\}\) by a sequence of transformations each of which is either an elementary Nielsen transformation or else consists of replacing some element by a conjugate. The author gives a proof of this conjecture in the variety of solvable groups.
scientific article; zbMATH DE number 3914562